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Subject: Preliminaries ×

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Now showing 1 - 3 of 3
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    Variety of Bicommutative Algebras defined by identity
    (Faculty of Engineering and Natural Science, 2022) Makhasheva A.
    One of the important questions in modern algebra is to study algebras satisfying certain identities. There are two questions in the theory of polynomial identities. The first is to describe an algebra by a defined identity. The second is to describe identities in algebra. The study of identities will help us in the construction of basis of free algebra, in the study of the Hilbert sequence, the Specht problem and problems of the finite basis. In this work, we used two different research methods. First, the theory of representations of symmetric groups. Second, the theory of representations of linear groups. In this research paper, we have completely described the subvariety of variety of bicommutative algebras defined by the identity α[(ab)c+(ba)c+(ca)b]+β[a(bc)+a(cb)+b(ca)]=0.
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    Hypoelliptic functional inequalities and applications
    (Faculty of Engineering and Natural Sciences, 2023) Seitkan M.
    In this thesis we discuss cylindrical extensions of the improved Rellich inequalities on R* x R"-* with the Euclidean norm |- |, on R*. Actually, we show sharp remainders of the Rellich type inequalities yielding the classical Rellich inequality. Moreover, Rellich type identities and inequalities with more general weights are established. In addition, we present horizontal extensions of these results on stratified Lie groups.
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    Functional inequalities on Lie groups and applications
    (Faculty of Engineering and Natural Sciences, 2023) Kalaman M.
    In this thesis we discuss sharp remainder formulae for the cylindrical extensions of the improved Hardy inequalities. For more general p we obtain cylindrical improved L?-Hardy identities for all real-valued functions f € Cg°(R"\{2x' = 0}), while in L? case we have them for any complex-valued function f € Cg°(R"\{z' = 0}). Moreover, we show cylindrical L?-Hardy inequalities for all complex-valued functions f € Cp°(IR"\{a’ = 0}). As applications, we establish Heisenberg-PaulWeyl type uncertainty principles and Caffarelli-Kohn-Nirenberg type inequalities. In particular cases, these inequalities imply new functional inequalities, which are not covered by the classical Caffarelli-Kohn-Nirenberg inequalities. Furthermore, the thesis contains L* and L? identities with logarithmic type functions on the quasi-ball B(0,R) with R > 0. In addition, we also discuss the results in the setting of homogeneous Lie groups.